scholarly journals The Journal of Mathematical Behavior

2019 ◽  
pp. 443-453 ◽  
Author(s):  
Carolyn A. Maher ◽  
Elizabeth Uptegrove ◽  
Louise C. Wilkinson
Keyword(s):  
Mathematical Behavior

Editorial comment: As we read

1969 ◽  
Vol 16 (1) ◽  
pp. 5-6
Keyword(s):  
Problem Solving ◽  
Editorial Comment ◽  
Mathematical Behavior

Rain is for feeling, sun is for warming, and problems are for solving! A meaningful problem cannot stand alone. It demands a solution and motivates the solver. The very essence of mathematical behavior is the solving of problems. The teacher of mathematics is faced with two questions when he considers the pedagogy of problem solving. How are meaningful problems developed? And how can a teacher foster good habits and techniques for problem solving? Exploration of these two questions generates the theme for this issue of The Arithmetic Teacher.

The Constructivist Researcher as Teacher and Model Builder

1983 ◽  
Vol 14 (2) ◽  
pp. 83-94 ◽  
Author(s):  
Paul Cobb ◽  
Leslie P. Steffe
Keyword(s):  
Mathematical Knowledge ◽  
Extended Period ◽  
Teaching Experiment ◽  
Constructivist Teaching ◽  
Individual Interviews ◽  
Model Builder ◽  
Mathematical Behavior ◽  
Constructivist Teaching Experiment

The constructivist teaching experiment is used in formulating explanations of children's mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time—anywhere from 6 weeks to 2 years. The explanations we formulate consist of models—constellations of theoretical constructs--that represent our understanding of children's mathematical realities. However, the models must be distinguished from what might go on in children's heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children's construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher's understanding of the children.

Beliefs and Their Influence on Mathematical Performance

1989 ◽  
Vol 82 (7) ◽  
pp. 502-505 ◽  
Author(s):  
Joe Garofalo
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Mathematical Tasks ◽  
Mathematical Task ◽  
Mathematical Content ◽  
Mathematical Performance ◽  
Mathematics Problems ◽  
Course Of Action ◽  
Mathematical Behavior ◽  
Research In Mathematics Education

Recent research in mathematics education has shown that success or failure in solving mathematics problems often depends on much more than the knowledge of requisite mathematical content. Knowing appropriate facts, algorithms, and procedures is not sufficient to guarantee success. Other factors, such as the decisions one makes and the strategies one uses in connect ion with the control and regulation of one's actions (e.g., deciding to analyze the conditions of a problem, planning a course of action, assessing progress), the emotions one fee ls while working on a mathematical task (e.g., anxiety, frustration, enjoyment), and the beliefs one holds relevant to performance on mathematical tasks, influence the direction and outcome of one's performance (Garofalo and Lester 1985; Schoenfe ld 1985; McLeod 1988). These other factors, although not explicitly addressed in typical mathematics instruction, are nonetheless important aspects of mathematical behavior.

Connecting Research to Teaching: Learning and Teaching Indirect Proof

1996 ◽  
Vol 89 (6) ◽  
pp. 474-482 ◽  
Author(s):  
Denisse R. Thompson
Keyword(s):  
Mathematics Education ◽  
Formal Proof ◽  
Learning And Teaching ◽  
Indirect Proof ◽  
Content Domain ◽  
Teaching Learning ◽  
Mathematical Behavior

Proof! It is the heart of mathematics as individuals explore, make conjectures, and try to convince themselves and others about the truth or falsity of their conjecture. In fact, proving is one of the main aspects of mathematical behavior and “most clearly distinguishes mathematical behavior from scientific behavior in other disciplines” (Dreyfus et al. 1990, 126). By its nature, proof should promote understanding and thus should be an important part of the curriculum (Hanna 1995). Yet students and teachers often find the study of proof difficult, and a debate within mathematics education is currently underway about the extent to which formal proof should play a role in geometry, the content domain in which reasoning is typically studied at an intensive level (Battista and Clements 1995).

PROPOSED ATTENUATION‐DISPERSION PAIR FOR SEISMIC WAVES

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 456-461 ◽  
Author(s):  
J. E. White ◽  
D. J. Walsh
Keyword(s):  
Experimental Data ◽  
Seismic Waves ◽  
Numerical Application ◽  
Low Frequencies ◽  
One Dimensional ◽  
Lumped Element ◽  
Resistive Element ◽  
The Hilbert Transform ◽  
Attenuation And Dispersion ◽  
Mathematical Behavior

Several papers in recent years have dealt with the causality‐imposed relation between attenuation and dispersion for waves in lossy solids, with emphasis on seismic waves. While the published formulas for dispersion within a particular frequency band are supported by experimental evidence within that band, the mathematical behavior of these expressions outside the band, particularly at low frequencies, is physically unacceptable. In the present paper, one‐dimensional seismic waves are modeled as propagation along a simple lumped‐element transmission line, leading to expressions for attenuation and velocity as functions of frequency which not only satisfy the experimental data available, but exhibit no objectionable behavior outside the range of available data. This is achieved by introducing a resistive element whose value is inversely proportional to frequency. Numerical application of the Hilbert transform shows the condition of causality to be satisfied by this model quite accurately.

PERFORMANCE ESTIMATION TOOLS FOR: DECOUPLING BY FILTERING OF TEMPERATURE AND EMISSIVITY (DEFILTE), AN ALGORITHM FOR THERMAL HYPERSPECTRAL IMAGE PROCESSING

2008 ◽  
Vol 18 (03) ◽  
pp. 675-699 ◽  
Author(s):  
PIERRE LAHAIE
Keyword(s):  
Image Processing ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Hyperspectral Image ◽  
Performance Estimation ◽  
Behavior Model ◽  
Hyperspectral Image Processing ◽  
Hyperspectral Sensors ◽  
Complete Procedure ◽  
Mathematical Behavior

The construction of very good hyperspectral sensors operating in the thermal infrared bands from 8 to 12 microns arouses much interest for the development of data exploitation tools. Temperature emissivity separation (TES) algorithms are very important components of a future toolbox, because they make it possible to extract these two fundamental targets’ parameters. The emissivity relies on the nature of the target's surface materials, while the temperature gives information related to their use and relationship with the environment. The TES technique presented in this paper is based on iteration on temperature principle, where a total square error criterion is used to estimate the temperature. The complete procedure is described in the paper. Its sensitivity to noise is studied and a mathematical behavior model is provided. The model is validated through a Monte-Carlo simulation of the technique's operation.

Distinct mathematical behavior of apoptotic versus non-apoptotic tumor cell death

1999 ◽  
Vol 43 (3) ◽  
pp. 601-605 ◽  
Author(s):  
Patricia Harrigan Hardenbergh ◽  
Philip Hahnfeldt ◽  
Lynn Hlatky ◽  
Clifford Takemoto ◽  
Akiko Shimamura ◽  
...  
Keyword(s):  
Cell Death ◽  
Tumor Cell ◽  
Tumor Cell Death ◽  
Apoptotic Tumor Cell ◽  
Mathematical Behavior

Alumina Porous Ceramics: Mathematical Behavior at Different Commercial Starch Concentration

2008 ◽  
Vol 591-593 ◽  
pp. 442-447 ◽  
Author(s):  
Rodrigo Sampaio Fernandes ◽  
Élson de Campos ◽  
José Luiz Minatti ◽  
Jerusa Góes Aragão Santana ◽  
Rogério Pinto Mota
Keyword(s):  
Porous Ceramics ◽  
Mechanical Resistance ◽  
Flexural Test ◽  
Exponential Equation ◽  
Weibull Statistics ◽  
Starch Concentration ◽  
First Order ◽  
Porosity Effect ◽  
Mathematical Behavior ◽  
Starch Consolidation

Several researches have been developed in order to verify the porosity effect over the ceramic material properties. The starch consolidation casting (SCC) allows to obtain porous ceramics by using starch as a binder and pore forming element. This work is intended to describe the porous mathematical behavior and the mechanical resistance at different commercial starch concentration. Ceramic samples were made with alumina and potato and corn starches. The slips were prepared with 10 to 50 wt% of starch. The specimens were characterized by apparent density measurements and three-point flexural test associated to Weibull statistics. Results indicated that the porosity showed a first-order exponential equation e-x/c increasing in both kinds of starches, so it was confirmed that the alumina ceramic porosity is related to the kind of starch used.

A Theory of Mathematical Knowledge: Can Rules Account for Creative Behavior?

1971 ◽  
Vol 2 (3) ◽  
pp. 183-196
Author(s):  
Joseph M. Scandura
Keyword(s):  
Mathematical Knowledge ◽  
Semantic Knowledge ◽  
Higher Order ◽  
Main Argument ◽  
Creative Behavior ◽  
Finite Set ◽  
Rule Sets ◽  
Mathematical Behavior ◽  
Mathematical Systems

This paper describes some elements of an emerging theory of mathematical knowledge. It is proposed that the mathematical behavior any given (idealized) S is potentially capable of at any given stage of learning can be accounted for precisely in terms of a finite set of rules. In particular, it is hypothesized that rule characterizations of this sort can account for creative, as well as more routine, behavior. The main argument centers on the notion of allowing rules to operate on other rules (i.e., to act as higher order rules) and thus allowing rule sets to “grow.” (Newly generated rules are assumed to be available from then on.) Attention is first centered on the behaviors involved in knowing mathematical systems (semantic knowledge). Then, the same ideas are extended to logical interrelationships between properties of mathematical systems, e.g., proving theorems.

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